Finite Group Databasebeta

← #8091774

Subgroups — #8091774

Order 512.

5053 conjugacy classes of subgroups.

The subgroup lattice has 975 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46275C214yesmaximal, complemented
2#46225C212yesmaximal, complemented
3#46196C212yesmaximal, complemented
4#46152C211yesmaximal, characteristic, complemented
5#46042C214yesmaximal, complemented
6#46026C218yesmaximal, complemented
7#46015C212yesmaximal, complemented
8#45986C214yesmaximal, complemented
9#45741C214yesmaximal, complemented
10#45600C214yesmaximal, complemented
11#45599C212yesmaximal, complemented
12#45542C218yesmaximal, complemented
13#36426C212yesmaximal, complemented
14#36412C212yesmaximal, complemented
15#36252C214yesmaximal, complemented
16#36235C214yesmaximal, complemented
17#36174C212yesmaximal, complemented
18#36125C211yesmaximal, characteristic, complemented
19C4×H(3,𝔽4)C211yesmaximal, characteristic, complemented
20#34346C212yesmaximal, complemented
21C2×H(3,𝔽4)C2211yescharacteristic
22C2×#555C2212yes—
23C2×#550C2211yescharacteristic, complemented
24C2×#547C2211yescharacteristic
25C2×#532C2212yes—
26C22×#117C2212yescomplemented
27#2864C2214yescomplemented
28#2859C2212yescomplemented
29#2858C2211yescharacteristic, complemented
30#2858C2212yescomplemented
31#2856C2214yes—
32#2853C2214yescomplemented
33#2853C2218yescomplemented
34#2850C2214yes—
35#2850C2218yes—
36#2850C2212yescomplemented
37#2847C2214yescomplemented
38#2847C2212yescomplemented
39#2844C2212yescomplemented
40#2830C2214yes—
41#2829C2218yescomplemented
42#2826C2214yescomplemented
43#2825C2218yes—
44#2819C2214yes—
45#2809C2212yescomplemented
46#2808C2214yescomplemented
47#2797C2218yescomplemented
48#2793C2218yescomplemented
49#2789C2214yescomplemented
50#2778C2218yescomplemented
51#2761C2218yescomplemented
52#2759C2218yescomplemented
53#2749C2218yescomplemented
54#2731C2214yes—
55#2730C2218yescomplemented
56#2720C2218yescomplemented
57#2711C2218yescomplemented
58#2710C2218yescomplemented
59#2709C2218yes—
60#2700C2218yescomplemented
61#2688C2218yes—
62#2688C2218yes—
63#2686C2218yescomplemented
64#2683C2212yes—
65#2682C2214yes—
66#2678C2218yescomplemented
67#2676C2218yes—
68#2676C2218yes—
69#2669C2214yes—
70#2669C2218yes—
71#2668C2214yescomplemented
72#2610C2218yes—
73#2609C2218yescomplemented
74#2595C2218yescomplemented
75#2580C2214yescomplemented
76#2576C2218yescomplemented
77#2567C2212yescomplemented
78#2555C2218yescomplemented
79#2555C2218yescomplemented
80#2546C2211yescharacteristic, complemented
81#2541C2211yescharacteristic
82#2541C2212yes—
83#2538C2212yescomplemented
84#2537C2212yes—
85#2535C2214yes—
86#2527C2218yescomplemented
87#2526C2218yescomplemented
88#2518C2218yescomplemented
89#2517C2218yescomplemented
90#2504C2212yescomplemented
91#2500C2214yescomplemented
92#2500C2214yescomplemented
93#2497C2214yescomplemented
94#2495C2214yescomplemented
95#2494C2214yescomplemented
96#2490C2214yes—
97#2489C2214yescomplemented
98#2487C2212yes—
99#2485C2214yes—
100#2477C2218yescomplemented
101#2476C2218yes—
102#2474C2218yescomplemented
103#2472C2218yescomplemented
104#2471C2218yes—
105#2471C2218yes—
106#2464C2218yescomplemented
107#2459C2218yes—
108#2440C2214yescomplemented
109#2439C2214yescomplemented
110#2439C2214yescomplemented
111#2432C2212yescomplemented
112#2431C2212yes—
113#2431C2214yes—
114#2428C2214yescomplemented
115#2428C2214yescomplemented
116#2428C2214yescomplemented
117#2424C2218yes—
118#2422C2214yescomplemented
119#2420C2214yescomplemented
120#2420C2214yescomplemented
121#2416C2214yes—
122#2414C2214yes—
123#2414C2214yes—
124#2411C2214yescomplemented
125#2404C2214yes—
126#2381C2214yescomplemented
127#2380C2214yes—
128#2379C2211yescharacteristic
129#2379C2212yes—
130#2379C2212yes—
131#2379C2212yes—
132#2379C2214yes—
133#2379C2214yescomplemented
134#2377C2218yescomplemented
135#2377C2218yescomplemented
136#2375C2212yes—
137#2375C2214yes—
138#2363C2214yescomplemented
139#2363C2214yescomplemented
140#2361C2214yescomplemented
141#2355C2212yescomplemented
142#2354C2212yes—
143#2352C2214yes—
144#2346C2214yescomplemented
145#2344C2212yescomplemented
146C4×#124C2211yescharacteristic
147C4×#124C2212yes—
148C4×#124C2212yes—
149C4×#124C2214yes—
150C4×#120C2212yes—
151C4×#120C2214yes—
152#2297C2214yes—
153#2297C2214yescomplemented
154#2290C2218yescomplemented
155#2290C2218yescomplemented
156#2283C2214yescomplemented
157C42×D4C2211yescharacteristic, complemented
158C42×D4C2212yescomplemented
159C22×#41C2312yes—
160C22×#41C2312yes—
161C24×C4C2312yes—
162H(3,𝔽4)—28no—
163#555—48no—
164#550—44no—
165#547—44no—
166#532—216no—
167C2×C4⋊Q8C2312yes—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2311yescharacteristic
170C2×#127C2312yes—
171C2×#127C2312yes—
172C2×#127C2311yescharacteristic
173C2×#127C2314yes—
174C2×#125C2314yes—
175C2×#124C2312yes—
176C2×#124C2312yes—
177C2×#124C2314yes—
178C2×#124C2312yes—
179C2×#124C2318yes—
180C2×#124C2318yes—
181C2×#124C2312yes—
182C2×#124C2311yescharacteristic
183C2×#123C2314yes—
184C2×#123C2318yes—
185C2×C22⋊Q8C2312yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2318yes—
188C2×#121C2318yes—
189C2×#121C2314yes—
190C2×#121C2314yes—
191C2×#121C2314yes—
192C2×#121C2312yes—
193C2×#121C2314yes—
194C2×#121C2312yes—
195C2×#121C2314yes—
196C2×#121C2314yes—
197C2×#121C2314yes—
198C2×#121C2318yes—
199C2×#121C2318yes—
200C2×#121C2318yes—
201C2×#120C2312yes—
202C2×#120C2314yes—
203C2×#120C2314yes—
204C2×#120C2318yes—
205C2×C4×Q8C2311yescharacteristic
206C2×C4×Q8C2312yes—
207C2×C4×D4C2312yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2311yescharacteristic
210C2×C4×D4C2314yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2312yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2311yescharacteristic
215C2×C4×D4C2312yes—
216C2×#117—48no—
217C2×#117C2314yes—
218C2×#117C2314yes—
219C2×#117C2318yes—
220C2×#117C2314yes—
221C2×#117C2314yes—
222C22×C4⋊C4C2312yes—
223C22×C4⋊C4C2312yes—
224C22×C22⋊C4C2314yes—
225C22×C42C2312yes—
226C22×C42C2314yes—
227C22×C42C2314yes—
228#401C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2314yes—
232#399C2314yes—
233#399C2318yes—
234#398C2318yes—
235#398C2314yes—
236#397C2318yes—
237#397C2318yes—
238#397C2318yes—
239#397C2318yes—
240#397C2318yes—
241#397C2318yes—
242#397C2318yes—
243#397C2318yes—
244#396C2318yes—
245#396C2318yes—
246#396C2318yes—
247#396C2318yes—
248#396C2318yes—
249#395C2314yes—
250#395C2314yes—
251#395C2318yes—
252#394C2318yes—
253#394C2318yes—
254#394C2318yes—
255#394C2318yes—
256#394C2318yes—
257#394C2318yes—
258#394C2318yes—
259#394C2318yes—
260#394C2318yes—
261#394C2318yes—
262#394C2318yes—
263#394C2318yes—
264#394C2318yes—
265#393C2318yes—
266#393C2318yes—
267#393C2318yes—
268#392C2318yes—
269#392C2318yes—
270#392C2318yes—
271#392C2318yes—
272#392C2318yes—
273#392C2318yes—
274#392C2314yes—
275#392C2318yes—
276#391C2314yes—
277#391C2314yes—
278#391C2318yes—
279#391C2312yes—
280#391C2312yes—
281#391C2311yescharacteristic
282#391C2314yes—
283#391C2312yes—
284#391C2318yes—
285#390C2314yes—
286#390C2312yes—
287#390C2314yes—
288#390C2314yes—
289#390C2314yes—
290#390C2318yes—
291#390C2312yes—
292#390C2318yes—
293#390C2318yes—
294#390C2314yes—
295#390C2314yes—
296#390C2314yes—
297#390C2314yes—
298#390C2312yes—
299#390C2311yescharacteristic
300#390C2318yes—
301#390C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2314yes—
310#388C2314yes—
311#388C2314yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2314yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2314yes—
327#388C2314yes—
328#388C2314yes—
329#388C2314yes—
330#388C2314yes—
331#388C2314yes—
332#388C2318yes—
333#388C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#386C2314yes—
347#386C2314yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2314yes—
361#386C2314yes—
362#386C2312yes—
363#386C2314yes—
364#386C2314yes—
365#386C2314yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2314yes—
370#386C2318yes—
371#385C2312yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2314yes—
376#385C2314yes—
377#385C2314yes—
378#385C2318yes—
379#385C2318yes—
380#385C2314yes—
381#385C2314yes—
382#384C2314yes—
383#384C2312yes—
384#384C2312yes—
385#383C2318yes—
386#382C2314yes—
387#382C2318yes—
388#382C2314yes—
389#382C2311yescharacteristic
390#382C2314yes—
391#382C2312yes—
392#382C2312yes—
393#382C2314yes—
394#381C2314yes—
395#381C2318yes—
396#381C2318yes—
397#380C2312yes—
398#380C2314yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#379C2312yes—
405#379C2314yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2311yescharacteristic
412C4×C22⋊C4C2318yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2312yes—
415C4×C22⋊C4C2314yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424#376C2318yes—
425C43C2311yescharacteristic
426C43C2312yes—
427C25C2412yes—
428C2×#41—28no—
429C2×#41—28no—
430C2×#41—44no—
431C2×#41—44no—
432C2×#41—82no—
433C2×#41—82no—
434C22×Q8C2412yes—
435C22×Q8C2412yes—
436C22×Q8C2414yes—
437C22×Q8C2411yescharacteristic
438C22×D4C2412yes—
439C22×D4C2411yescharacteristic
440C22×D4C2412yes—
441C22×D4C2414yes—
442C22×D4C2412yes—
443C22×D4C2418yes—
444C22×D4C2414yes—
445C22×D4C2414yes—
446C22×D4C2412yes—
447C22×D4C2418yes—
448C22×D4C2418yes—
449C22×D4C2418yes—
450C22×D4C2412yes—
451C22×D4C2414yes—
452C22×D4C2411yescharacteristic
453C23×C4—44no—
454C23×C4—48no—
455C23×C4C2412yes—
456C23×C4C2414yes—
457C23×C4C2414yes—
458C23×C4C2414yes—
459C23×C4C2412yes—
460C23×C4C2414yes—
461C23×C4C2414yes—
462C23×C4C2414yes—
463C23×C4C2418yes—
464C23×C4C2412yes—
465C4⋊Q8—28no—
466C4⋊Q8—42no—
467C4⋊Q8—44no—
468#127—28no—
469#127—44no—
470#127—42no—
471#127—84no—
472#125—84no—
473#124—28no—
474#124—216no—
475#124—28no—
476#124—28no—
477#124—416no—
478#124—88no—
479#124—82no—
480#124#4118yes—
481#123—48no—
482#123—88no—
483C22⋊Q8—44no—
484C22⋊Q8—88no—
485C22⋊Q8—84no—
486#121—232no—
487#121—48no—
488#121—44no—
489#121—48no—
490#121—48no—
491#121—48no—
492#121—48no—
493#121—44no—
494#121—48no—
495#121—84no—
496#121—88no—
497#121—88no—
498#121—88no—
499#120—28no—
500#120—216no—
501#120—84no—
502#120—88no—
503C4×Q8—44no—
504C4×Q8—42no—
505C4×D4—24no—
506C4×D4—28no—
507C4×D4—232no—
508C4×D4—48no—
509C4×D4—44no—
510C4×D4—48no—
511C4×D4—44no—
512C4×D4—42no—
513C4×D4—44no—
514#117—216no—
515#117—48no—
516#117—416no—
517#117—48no—
518#117—84no—
519C2×C4⋊C4—28no—
520C2×C4⋊C4—44no—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2418yes—
531C2×C4⋊C4C2411yescharacteristic
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2411yescharacteristic
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2411yescharacteristic
548C2×C22⋊C4—48no—
549C2×C22⋊C4C2418yes—
550C2×C22⋊C4C2412yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2418yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2414yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2418yes—
558C2×C22⋊C4C2412yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2412yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2414yes—
586C2×C42—28no—
587C2×C42—48no—
588C2×C42—84no—
589C2×C42C2418yes—
590C2×C42C2412yes—
591C2×C42C2411yescharacteristic
592C2×C42C2414yes—
593C2×C42C2412yes—
594C2×C42C2414yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2418yes—
598C2×C42C2418yes—
599C2×C42C2414yes—
600C2×C42C2411yescharacteristic
601C2×C42C2412yes—
602C2×C42C2414yes—
603C2×C42C2412yes—
604C2×C42C2411yescharacteristic
605#95C2414yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2414yes—
610#95C2414yes—
611#95C2418yes—
612#95C2414yes—
613#95C2414yes—
614#95C2412yes—
615#95C2418yes—
616#95C2414yes—
617#95C2414yes—
618#95C2418yes—
619#95C2414yes—
620#95C2418yes—
621#95C2414yes—
622#95C2414yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2418yes—
628#95C2414yes—
629#95C2418yes—
630#95C2418yes—
631#95C2418yes—
632#95C2418yes—
633C24—24no—
634C24—42no—
635C24—44no—
636C24—42no—
637C24—44no—
638C24C2514yes—
639C24C2514yes—
640C24C2512yes—
641C24C2512yes—
642#41—816no—
643#41—816no—
644C2×Q8—24no—
645C2×Q8—24no—
646C2×Q8—41no—
647C2×Q8—41no—
648C2×Q8—42no—
649C2×Q8—42no—
650C2×Q8—42no—
651C2×Q8—42no—
652C2×Q8—48no—
653C2×Q8—44no—
654C2×Q8C2×#4114yes—
655C2×D4—216no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—28no—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—28no—
666C2×D4—41no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—44no—
671C2×D4—48no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—42no—
676C2×D4—48no—
677C2×D4—42no—
678C2×D4—44no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—44no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4C2×#4114yes—
696C22×C4—28no—
697C22×C4—24no—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—24no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—42no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—44no—
715C22×C4—42no—
716C22×C4—44no—
717C22×C4—48no—
718C22×C4—44no—
719C22×C4—48no—
720C22×C4—48no—
721C22×C4—44no—
722C22×C4—48no—
723C22×C4—432no—
724C22×C4C2514yes—
725C22×C4C2514yes—
726C22×C4C2514yes—
727C22×C4C2518yes—
728C22×C4C2512yes—
729C22×C4C2514yes—
730C22×C4C2512yes—
731C22×C4C2514yes—
732C22×C4C2518yes—
733C22×C4C2512yes—
734C22×C4C2511yescharacteristic
735C22×C4C2511yescharacteristic
736C22×C4C2512yes—
737C22×C4C2512yes—
738C22×C4C2512yes—
739C22×C4C2511yescharacteristic
740C4⋊C4—216no—
741C4⋊C4—24no—
742C4⋊C4—28no—
743C4⋊C4—28no—
744C4⋊C4—24no—
745C4⋊C4—28no—
746C4⋊C4—44no—
747C4⋊C4—42no—
748C4⋊C4—44no—
749C4⋊C4—48no—
750C4⋊C4—42no—
751C4⋊C4—44no—
752C4⋊C4—41no—
753C4⋊C4—42no—
754C4⋊C4—44no—
755C4⋊C4—42no—
756C4⋊C4—41no—
757C4⋊C4—48no—
758C4⋊C4—48no—
759C4⋊C4—44no—
760C4⋊C4—48no—
761C4⋊C4—44no—
762C4⋊C4—44no—
763C4⋊C4—48no—
764C4⋊C4—42no—
765C4⋊C4—44no—
766C4⋊C4H(5,𝔽2)14yes—
767C22⋊C4—24no—
768C22⋊C4—216no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—216no—
773C22⋊C4—24no—
774C22⋊C4—28no—
775C22⋊C4—48no—
776C22⋊C4—48no—
777C22⋊C4—42no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—48no—
784C22⋊C4—42no—
785C22⋊C4—44no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—48no—
791C22⋊C4—48no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—48no—
799C22⋊C4—44no—
800C22⋊C4—48no—
801C22⋊C4—44no—
802C22⋊C4—48no—
803C22⋊C4C2×#41116yes—
804C42—28no—
805C42—24no—
806C42—24no—
807C42—216no—
808C42—24no—
809C42—22no—
810C42—24no—
811C42—28no—
812C42—48no—
813C42—42no—
814C42—48no—
815C42—44no—
816C42—41no—
817C42—44no—
818C42—42no—
819C42C2×#4114yes—
820C23—22no—
821C23—24no—
822C23—22no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—22no—
827C23—24no—
828C23—22no—
829C23—24no—
830C23—24no—
831C23—28no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—28no—
840C23—22no—
841C23—48no—
842C23—84no—
843C23—88no—
844C23—88no—
845C23—84no—
846C23C22×#4114yes—
847C23C2611yescharacteristic
848Q8—44no—
849Q8—84no—
850Q8—84no—
851Q8—164no—
852D4—44no—
853D4—44no—
854D4—48no—
855D4—84no—
856D4—84no—
857D4—84no—
858D4—88no—
859D4—816no—
860D4—88no—
861D4—88no—
862D4—168no—
863D4—168no—
864D4—168no—
865D4—162no—
866D4—164no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—21no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—28no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—24no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—28no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—28no—
894C2×C4—22no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—28no—
903C2×C4—28no—
904C2×C4—28no—
905C2×C4—416no—
906C2×C4—48no—
907C2×C4—416no—
908C2×C4—48no—
909C2×C4—416no—
910C2×C4—48no—
911C2×C4—416no—
912C2×C4—88no—
913C2×C4—816no—
914C2×C4—88no—
915C2×C4C22×#4114yes—
916C2×C4C22×#4112yes—
917C2×C4C22×#4114yes—
918C2×C4C2×H(5,𝔽2)14yes—
919C2×C4C2×H(5,𝔽2)12yes—
920C2×C4#58514yes—
921C22—24no—
922C22—28no—
923C22—44no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—48no—
931C22—44no—
932C22—44no—
933C22—48no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—42no—
939C22—44no—
940C22—44no—
941C22—42no—
942C22—44no—
943C22—816no—
944C22C23×#4111yescharacteristic
945C22C22×H(5,𝔽2)11yescharacteristic
946C22C2×#58512yes—
947C22H(7,𝔽2)11yescharacteristic
948C22H(7,𝔽2)12yes—
949C4—24no—
950C4—22no—
951C4—24no—
952C4—24no—
953C4—44no—
954C4—44no—
955C4—44no—
956C4—42no—
957C4—44no—
958C4—48no—
959C4—48no—
960C4—41no—
961C4—42no—
962C4—44no—
963C4—42no—
964C4#352914yes—
965C2—44no—
966C2—82no—
967C2—84no—
968C2—84no—
969C2C2×#352911yescharacteristic
970C2#6298311yescharacteristic
971C2#6299412yes—
972C2#6305112yes—
973C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #46275C2semidirect
2. #46225C2semidirect
3. #46196C2semidirect
4. #46152C2semidirect
5. #46042C2semidirect
6. #46026C2semidirect
7. #46015C2semidirect
8. #45986C2semidirect
9. #45741C2semidirect
10. #45600C2semidirect
11. #45599C2semidirect
12. #45542C2semidirect
13. #36426C2semidirect
14. #36412C2semidirect
15. #36252C2semidirect
16. #36235C2semidirect
17. #36174C2semidirect
18. #36125C2semidirect
19. C4×H(3,𝔽4)C2semidirect
20. #34346C2semidirect
23. C2×#550C22semidirect
26. C22×#117C22semidirect
27. #2864C22semidirect
28. #2859C22semidirect
29. #2858C22semidirect
30. #2858C22semidirect
32. #2853C22semidirect
33. #2853C22semidirect
36. #2850C22semidirect
37. #2847C22semidirect
38. #2847C22semidirect
39. #2844C22semidirect
41. #2829C22semidirect
42. #2826C22semidirect
45. #2809C22semidirect
46. #2808C22semidirect
47. #2797C22semidirect
48. #2793C22semidirect
49. #2789C22semidirect
50. #2778C22semidirect
51. #2761C22semidirect
52. #2759C22semidirect
53. #2749C22semidirect
55. #2730C22semidirect
56. #2720C22semidirect
57. #2711C22semidirect
58. #2710C22semidirect
60. #2700C22semidirect
63. #2686C22semidirect
66. #2678C22semidirect
71. #2668C22semidirect
73. #2609C22semidirect
74. #2595C22semidirect
75. #2580C22semidirect
76. #2576C22semidirect
77. #2567C22semidirect
78. #2555C22semidirect
79. #2555C22semidirect
80. #2546C22semidirect
83. #2538C22semidirect
86. #2527C22semidirect
87. #2526C22semidirect
88. #2518C22semidirect
89. #2517C22semidirect
90. #2504C22semidirect
91. #2500C22semidirect
92. #2500C22semidirect
93. #2497C22semidirect
94. #2495C22semidirect
95. #2494C22semidirect
97. #2489C22semidirect
100. #2477C22semidirect
102. #2474C22semidirect
103. #2472C22semidirect
106. #2464C22semidirect
108. #2440C22semidirect
109. #2439C22semidirect
110. #2439C22semidirect
111. #2432C22semidirect
114. #2428C22semidirect
115. #2428C22semidirect
116. #2428C22semidirect
118. #2422C22semidirect
119. #2420C22semidirect
120. #2420C22semidirect
124. #2411C22semidirect
126. #2381C22semidirect
133. #2379C22semidirect
134. #2377C22semidirect
135. #2377C22semidirect
138. #2363C22semidirect
139. #2363C22semidirect
140. #2361C22semidirect
141. #2355C22semidirect
144. #2346C22semidirect
145. #2344C22semidirect
153. #2297C22semidirect
154. #2290C22semidirect
155. #2290C22semidirect
156. #2283C22semidirect
157. C42×D4C22semidirect
158. C42×D4C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#462752
#462252
#461962
#461522
#460422
#460262
#460152
#459862
#457412
#456002
#455992
#455422
#364262
#364122
#362522
#362352
#361742
#361252
C4×H(3,𝔽4)2
#343462